Problem: The function $f(x)$ satisfies
\[xf(y) = yf(x)\]for all real numbers $x$ and $y.$  If $f(15) = 20,$ find $f(3).$
Answer: Setting $y = 3$ and $x = 15,$ we get
\[15f(3) = 3f(15) = 60,\]so $f(3) = \boxed{4}.$